A Theoretical and Numerical Study on the Exponential Stabilization of the Rotating Disk–Beam System With a Boundary Delay: A Nonclassical Case

Abstract

ABSTRACT This paper investigates the stabilization problem of the rotating disk–beam system. The boundary control includes a delayed velocity term, while the compensating term involves the angular velocity, differing from common formulations in the literature. Despite this nonstandard setting, we demonstrate that the problem is well‐posed under certain assumptions on the system's physical parameters. Additionally, the exponential stability of the system is established. Finally, using a finite difference method, numerical results are presented to support the theoretical findings.